Efficient methods for linear Schrödinger equation in the semiclassical regime with time-dependent potential

Abstract

We build efficient and unitary (hence stable) methods for the solution of the linear time-dependent Schrödinger equation with explicitly time-dependent potentials in a semiclassical regime. The Magnus–Zassenhaus schemes presented here are based on a combination of the Zassenhaus decomposition (Bader et al. 2014 Found. Comput. Math. 14 , 689–720. ( doi:10.1007/s10208-013-9182-8 )) with the Magnus expansion of the time-dependent Hamiltonian. We conclude with numerical experiments.